I’m interested in various topics in arithmetic geometry, like ranks of elliptic curves over function fields, curves over finite fields, Jacobian varieties
and Galois representations.
- Vanishing of Hyperelliptic L-Functions at the Central
Point, J. Number Theory 191 (2018), 85-103.
- Effective Bounds on the Dimensions of Jacobians Covering Abelian Varieties (Joint with Juliette Bruce), Proc. Amer. Math. Soc. 148 (2020), no. 2, 535-551
- Newton polygons of cyclic covers of the projective line branched at three points (Joint with Elena Mantovan, Rachel Pries, Yunqing Tang), Research Directions in Number Theory: Women in Numbers IV.
- Newton Polygons Arising for Special Families of Cyclic Covers of the Projective Line (Joint with Elena Mantovan, Rachel Pries, Yunqing Tang), Res. Number Theory 5 (2019), no. 1
- Ranks, 2-Selmer groups, and Tamagawa numbers of elliptic curves with Z/2ZxZ/8Z-torsion (Joint with Stephanie Chan, Jeroen Hanselman), ANTS XIII
- Newton Polygon Stratification of the Torelli Locus in PEL-type Shimura Varieties (Joint with Elena Mantovan, Rachel Pries, Yunqing Tang), to appear in IMRN
- Nonvanishing of hyperelliptic zeta functions over finite fields (Joint with Jordan Ellenberg, Mark Shusterman), Algebra Number Theory 14 (2020), no. 7, 1895-1909.
- Group-theoretic Johnson classes and a non-hyperelliptic curve with torsion Ceresa class (Joint with Dean Bisogno, Daniel Litt, Padmavathi Srinivasan), submitted
- The Ceresa class: tropical, topological, and algebraic (Joint with Daniel Corey, Jordan Ellenberg), submitted
- Surface bundles and the section conjecture (Joint with Daniel Litt, Nick Salter, Padmavathi Srinivasan), submitted
- Vanishing of Dirichlet L-functions at the central point over function fields (Joint with Ravi Donepudi), submitted
- Doubly isogenous genus-2 curves with D_4-action (Joint with Vishal Arul, Jeremy Booher, Steven R. Groen, Everett W. Howe, Vlad Matei, Rachel Pries, Caleb Springer), submitted
- Data for Shimura varieties intersecting the Torelli locus (Joint with Elena Mantovan, Rachel Pries)
- Abelian varieties of prescribed order over finite fields (Joint with Raymond van Bommel, Edgar Costa, Bjorn Poonen, Alexander Smith)
Slides and Poster
- Elliptic curves with rational Z2xZ8-torsion
- Slides: Vanishing of Hyperelliptic L-Functions at the Central
- Slides: Effective Bounds on the Dimensions of Jacobians
Covering Abelian Varieties